The act of not obtaining medical attention after sustaining an injury to any part of one's body and leaving the wound to heal via the natural medicinal properties of normal air, and the body's own healing mechanisms. If anything is used to clean, cover, or assist/speed up the healing process, it is no longer deeming 'air healing' and you will be made fun of accordingly.
Seth: "DUDE! How did get that gash in your leg?"
Jon: "I tripped over the bonfire on my way to get the bong... I think I need stitches."
Seth: "Should I drive you to the hospital?"
Jon: "Naw... I'm just going to let it air heal."
Seth: "Sweet. Your pack btw."